Revolt against austerity is sweeping Europe. The election of François Hollande has not only opened up the chance of a change of direction in France, but even in the citadels of fiscal orthodoxy in Brussels, Frankfurt and Berlin. In Greece, Sunday's electoral earthquake has all but destroyed the political establishment that dominated the country for 40 years.

From the Netherlands to Romania, governments are falling under the weight of cuts and tax rises required by the eurozone's new permanent deflation treaty. In Ireland, the anti-austerity tide is swelling support for a no vote in this month's treaty referendum.

And it's not difficult to see why they're rejecting it. Austerity isn't working, even in its own terms. Cutting jobs and pay while increasing taxes isn't reducing borrowing and debt, let alone leading to economic recovery. It's deepening recession, increasing debt and destroying jobs and squeezing living standards across the eurozone – in countries such as Spain and Greece, catastrophically – as well as in Britain.

David Cameron and Nick Clegg today took the opportunity of their defeat in last week's local elections to insist there could be no "let-up" in their own austerity programme. That comes less than a fortnight after the country officially sank into a double-dip recession as cuts shrank the construction sector.

Of course they also insisted they would "go for growth". But as voters across Europe are about to discover, growth policies come in all shapes and sizes, from deregulation to public investment, and the inclusion of plans to make it easier to sack workers in tomorrow's Queen's speech makes quite clear which kind Cameron and Clegg have in mind.

The political upheaval in Greece, however, could have still more far-reaching consequences. Greece's economic collapse, triggered by the crash of 2008 and deepened by EU and IMF-enforced austerity, is a social disaster on the level of the US depression of the 1930s. Real wages have fallen by 25% in two years, according to the OECD.

It's hardly surprising that support for the governing parties which brought Greece to such a pass fell from 80% to 30%, while leftwing parties that reject the EU-IMF cuts, privatisations and unachievable debt repayments surged ahead of both the discredited establishment and the nationalist right.

While international attention has focused on the fascist Golden Dawn party's 7% vote, by far the biggest beneficiary of Sunday's election was the radical left Syriza coalition, which won 17%. Its leader Alexis Tsipras has been holding talks on the unlikely prospect of forming a government without new elections.

For the past four years, the crisis has culled incumbents without discrimination, from the Republican George Bush and conservative Nicolas Sarkozy to Labour's Gordon Brown and the Spanish Socialist José Luis Zapatero, while the far right has advanced across Europe by preying on anti-migrant insecurities and posing as anti-establishment outsiders.

It is now being challenged by parties of the left that reject a failing neoliberal system and are retaking social territory which should never have abandoned. Marine Le Pen's National Front outpolled Jean-Luc Mélenchon's Left Front in France's presidential elections. But it's not Geert Wilders' Islamophobic Freedom party that has gained most from the collapse of the pro-austerity Dutch government, it's the radical Socialist party, now coming first or second in opinion polls with up to 20% support.

As the cost of the establishment's austerity deepens, the polarisation between left and right is portrayed in much of the media as the rise of "extremes". But it's both absurd and repugnant to equate racist or xenophobic nationalists, which have kept supposedly centrist governments in power from Denmark to Italy, with leftist parties rooted in social movements that stand for a progressive political and economic alternative.

Nor is there anything "extreme" about an organisation such as Syriza that rejects a programme of social and economic destruction which is in every sense extreme – and calls for negotiation. Mainstream political choices and debates have become so narrow over the years of pro-market consensus that the reappearance of genuine alternatives is apparently too shocking to absorb.

The expectation is now that Merkel will block attempts by Hollande to renegotiate Europe's austerity treaty, but instead agree to add a vaguely worded growth pact (as happened in the runup to the creation of the euro in the 90s) that would allow extra European Investment Bank lending and infrastructure projects.

If the French Socialist president were then to drive through the kind of cuts implied by his plans to balance the budget by 2017, in a context of continuing eurozone crisis and slump, the risk of fuelling a resurgent and toxic right on the back of social disillusionment is obvious. Either in that case – or of a clash with the financial markets – only a powerful social movement could provide the necessary counterweight.

The future of the eurozone now depends on what happens in Greece, and the risk of market contagion. Some on the Greek left hope to strengthen their bargaining hand with the EU and IMF in new elections. Others are sceptical, as the likelihood of default and exit from the euro looms ever larger.

Greece is a harsh case, where the political battle is now on between radical options of diametrically opposed kinds. But people across Europe are profoundly disillusioned with a market-driven order that has failed to deliver. If the left doesn't offer a real alternative, others certainly will – with ugly consequences.